Additive Reasoning and Problem-Solving

In this chapter we illustrate how a computer-assisted intervention program, COMPS-A that integrates a constructivist view of learning and explicit teaching of mathematical model-based problem-solving, can help students with learning disabilities or difficulties in mathematics. Building on students’ development of fundamental ideas such as “number as the composite unit” (which naturally leads to the part-part-whole additive relationships), COMPS-A emphasizes students’ understanding and representation of mathematics relations in algebraic equations and, thus, supports growth in generalized problem-solving skills. Findings from empirical studies indicate that elementary students with learning difficulties in mathematics can be expected to move beyond concrete operations and toward thinking symbolically or algebraically. Algebraic conceptualizations of mathematical relations and model-based problem-solving can be taught through systematic strategy instruction. Introducing symbolic representation and algebraic thinking in earlier grades may facilitate a smoother transition from elementary to higher level mathematics and improve middle- and high school mathematics performance.